Geodesic
A graph-based estimator of the number of clusters
ESAIM: Probability and Statistics, Tome 11 (2007), pp. 272-280 Cet article a éte moissonné depuis la source Numdam

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Assessing the number of clusters of a statistical population is one of the essential issues of unsupervised learning. Given n independent observations X 1 ,⋯,X n drawn from an unknown multivariate probability density f, we propose a new approach to estimate the number of connected components, or clusters, of the t-level set ℒ(t)={x:f(x)≥t}. The basic idea is to form a rough skeleton of the set ℒ(t) using any preliminary estimator of f, and to count the number of connected components of the resulting graph. Under mild analytic conditions on f, and using tools from differential geometry, we establish the consistency of our method.

DOI : 10.1051/ps:2007019
Classification : 62G05, 62G20
Keywords: cluster analysis, connected component, level set, graph, tubular neighborhood 
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     author = {Biau, G\'erard and Cadre, Beno{\^\i}t and Pelletier, Bruno},
     title = {A graph-based estimator of the number of clusters},
     journal = {ESAIM: Probability and Statistics},
     pages = {272--280},
     year = {2007},
     publisher = {EDP-Sciences},
     volume = {11},
     doi = {10.1051/ps:2007019},
     mrnumber = {2320821},
     zbl = {1187.62114},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2007019/}
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Biau, Gérard; Cadre, Benoît; Pelletier, Bruno. A graph-based estimator of the number of clusters. ESAIM: Probability and Statistics, Tome 11 (2007), pp. 272-280. doi: 10.1051/ps:2007019

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